A Jet Formation Criterion for Synthetic Jet Actuators

This paper proposes and validates a jet formation criterion for synthetic jet actuators. The synthetic jet is a zero net mass flux device, adding additional momentum but no mass to its surroundings. Jet formation is defined as a mean outward velocity along the jet axis and corresponds to the clear formation of shed vortices. It is shown that the synthetic jet formation is governed by the Strouhal number (or Reynolds number and Stokes number). Numerical simulations and experiments are performed to supplement available two-dimensional and axisymmetric jet formation data in the literature. The data support the jet formation criterion , where the constant 2 Re/ S K > K is approximately 2 and 0.16 for two dimensional and axisymmetric synthetic jets, respectively. This criterion is valid for relatively thick orifice plates with thickness-to-width ratios greater than approximately 2. This result is expected to be useful for the design of flow-control actuators and engine nacelle acoustic liners. Introduction Synthetic jet actuators have been shown to be a useful tool for flow control, with applications including mixing enhancement, separation control, and thrust vectoring [1]. Figure 1 shows a schematic of a typical synthetic jet or “zero net mass flux” device. In its most common implementation, a piezoelectric disk is bonded to a metal diaphragm, which is sealed to form a cavity. As the diaphragm oscillates, fluid is periodically entrained and expelled from the cavity through the orifice (or slot). Under certain operating conditions, a vortex pair (vortex ring in the axisymmetric case) is formed at the orifice edge during the expulsion part of the cycle. This vortex pair is convected away from the orifice. If the self-induced velocity of the vortex pair is strong enough, then the vortex pair is not ingested back into the orifice during the suction part of the cycle. The formation of a vortex pair is defined herein as the onset of jet formation.